The starting point for the statistical computations is the set of measured values—the frequencies stored in , *total-spams*, and *total-hams*. Assuming that the set of messages trained on is statistically representative, you can treat the observed frequencies as probabilities of the same features showing up in hams and spams in future messages.

The basic plan is to classify a message by extracting the features it contains, computing the individual probability that a given message containing the feature is a spam, and then combining all the individual probabilities into a total score for the message. Messages with many “spammy” features and few “hammy” features will receive a score near 1, and messages with many hammy features and few spammy features will score near 0.

The problem with the value computed by this function is that it’s strongly affected by the overall probability that any message will be a spam or a ham. For instance, suppose you get nine times as much ham as spam in general. A completely neutral feature will then appear in one spam for every nine hams, giving you a spam probability of 1/10 according to this function.

But you’re more interested in the probability that a given feature will appear in a spam message, independent of the overall probability of getting a spam or ham. Thus, you need to divide the spam count by the total number of spams trained on and the ham count by the total number of hams. To avoid division-by-zero errors, if either of or *total-hams* is zero, you should treat the corresponding frequency as zero. (Obviously, if the total number of either spams or hams is zero, then the corresponding per-feature count will also be zero, so you can treat the resulting frequency as zero without ill effect.)

However, it’s still quite possible that the feature that has appeared only once is actually a neutral feature—it’s obviously rare in either spams or hams, appearing only once in 2,000 messages. If you trained on another 2,000 messages, it might very well appear one more time, this time in a ham, making it suddenly a neutral feature with a spam probability of .5.

So it seems you might like to compute a probability that somehow factors in the number of data points that go into each feature’s probability. In his papers, Robinson suggested a function based on the Bayesian notion of incorporating observed data into prior knowledge or assumptions. Basically, you calculate a new probability by starting with an assumed prior probability and a weight to give that assumed probability before adding new information. Robinson’s function is this: